Non-equilibrium phase transition from AdS/CFT

Non-equilibrium phase
transition from AdS/CFT
Mohammad Ali-Akbari
School of particles and accelerators, IPM, Iran
Seventh Crete regional meeting on string theory
Kolymbari 2013

Outline
1. Non-equilibrium system: non-equilibrium steady sates.
2. Non-equilibrium phase transition of differential conductivity.
3. AdS/CFT correspondence + matter fields
4. Non-linear conductivity in the presence of magnetic field:
3.1: D3-D7 system.
3.2: D3-D5(supersymmetric and non-supersymmetrc) systems.

Non-equilibrium system
Challenging problem: Physical system at non-equilibrium phase.
1. Local equilibrium Hydrodynamics
2. Non-equilibrium steady states:
They have no macroscopically observable time dependence.
Y. Oono, and M. Paniconi, “Steady state thermodynamics,” Prog. Theor. Phys. Suppl. 130, 29--44 (1998
S. Sasa and H. Tasaki, ``Steady state thermodynamics,'' [cond-mat/0411052].
Z. Racz, ``Nonequilibrium phase transition,'' [cond-mat/0210435].
B. Derrida, ``Non equilibrium steady states: fluctuations and large deviations of the density and of the

Conductivity:
Non-linear conductivity:
Duo to the non-linearity of conductivity, differential conductivity may be
either positive or negative.
Positive differential conductivity(PDC)
Phase transition
Negative differential conductivity(NDC)
Strong interaction
AdS/CFT correspondence as a theoretical
framework
Y. Taguchi, T. Matsumoto, Y. Tokura, “Dielectric breakdown of one-dimensional Mott
insulators
Sr 2 CuO 3 and SrCuO 2 ,” Phys. Rev. B 62, 7015–7018 (2000)
Takashi Oka, Hideo Aoki, ” Nonequilibrium Quantum Breakdown in a Strongly

AdS/CFT correspondence
IIB string theory on
AdS(5)xS(5)
N=4 D=4 superconformal
Su(N) gauge theory
D3-D7:
D3
D7
Probe limit
AdS background + D7-brane
A. Karch and E. Katz, JHEP 0206, 043 (2002) [hep-th/
0205236].
Strongly coupled Su(N) gauge theory
+ fundametal matters

AdS background + D7-brane
(A reminder)
D7-brane is extended along .

Gauge theory side
Gravity side
1. Strongly coupled thermal field
theory.
2. Explicit charge carriers.
3. Electric and magnetic fileds.
1. BH -AdS Sch.
2. Time component of the gauge field
on the D7-branes ( ).
3. The spatial components of the
gauge field.
4. (non-linear)
Conductivity .
4.
Mass of the fundamental
matter
A. Karch and A. O'Bannon, ``Metallic AdS/CFT,‘’ JHEP 0709, 024 (2007), [arXiv:0705.3870 [hepth]].
A. O'Bannon, ``Hall Conductivity of Flavor Fields from AdS/CFT,‘’ Phys. Rev. D 76, 086007 (2007),

A. Karch and A. O'Bannon, ``Metallic AdS/CFT,‘’ JHEP 0709, 024 (2007), [arXiv:0705.3870 [hepth]].
A. O'Bannon, ``Hall Conductivity of Flavor Fields from AdS/CFT,‘’ Phys. Rev. D 76, 086007 (2007),
D7-branes action
Conductivity equations
Current
Asymptotic behaviour
Mass

Current
We need to solve the equation of motion for
its asymptotic value
for given E, B and temperature.
to find
S. Nakamura, ``Nonequilibrium Phase Transitions and Nonequilibrium Critical Point from
AdS/CFT,‘’
Phys. Rev. Lett. 109, 120602 (2012) [arXiv:1204.1971 [hep-th]].
S. Nakamura, ``Negative Differential Resistivity from Holography,‘’ Prog. Theor.
Phys. 124, 1105 (2010) [arXiv:1006.4105 [hep-th]].
M. Ali-Akbari and A. Vahedi, ``Non-equilibrium Phase Transition from AdS/CFT,‘’ arXiv
1305.3713 [hep-th].

: Insulator phase : Conductor phase

Small-J region: NDC
Large-J region: PDC
Blue curve : First order phase transition
Red curve: Second order phase transition
Green curve: Crossover

Hamiltonian
Energy
It numerically turns out that the solutions with the
largest value of the electric field have the lowest
energy.
A. Karch and A. O'Bannon, ``Metallic AdS/CFT,‘’ JHEP 0709, 024 (2007), [arXiv:0705.3870 [hepth]].
A. O'Bannon, ``Hall Conductivity of Flavor Fields from AdS/CFT,‘’ Phys. Rev. D 76, 086007 (2007),

D3-D5 systems
Supersymmetric
D3-D5
Current
2+1 dimensional subspace on which the matter fields live.

Non-supersymmetric
D3-D5
1+1 dimensional subspace on which the matter fields live.
Current

Results